It's the famously incompetent Japanese police we are talking about. I bet the murderer didn't need to do anything at all for the police to arrest and accuse Jun. The cops just catch the very first person who seems plausible and then force a confession out of him and/or railroad the case through so that they can tell the public the serial killer has been caught and someone within the police forces gets a promotion. It's inconsequential if the real killer is still at large or not.